Deplacement-Rotation Algorithmen

[Cubist]

Posted on behalf of @trojana

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Deplacement-Rotation Algorithmen​

The attached sketch shows an object which can move in x-y plane and rotate around z axis only. The movements are small and in the order of micrometers.

Point a, b and c are the locations of measurement. Each of these points have measuring devices which can give linear displacement in micrometers.

If the object is displaced by external force, the measuring devices will give linear displacement values. However, with these 3 displacement values, I would like to develop an algorithm which can give me overall displacement of the object along x and y axes as well rotation around z axis.

 

[blamocur]

However, with these 3 displacement values, I would like to develop an algorithm which can give me overall displacement of the object along x and y axes as well rotation around z axis.

I don't see how you can figure out the rotation if you can only measure the displacements.

 

[Dr.Peterson]

I see this was also asked at Physics Forums, but I think the answer there misunderstands the question (which, indeed, is not stated very clearly).

As I understand it, you are measuring only three quantities, the (change in) x-coordinate of points A and B, and the (change in) y-coordinate of point C. You want to find the (change in) x- and y-coordinates of the center of the object, and the angle of rotation. So there are 3 known values and three unknowns. Write equations for the three knowns, in terms of the three unknowns, and try to solve for the latter.

If you can show a picture of your work, we will probably have a better idea of what you are doing.